Earlier quoted context omitted.
The market does not work that way. You're implying that the cause and effect are backwards. It is local wages that set the price! The prices, while they do adjust slowly due to high friction in the housing market, are not exogenous.
The 500% difference in housing prices. You are leaving out numerous factors including demand, supply, and local regulations.
Curiously, 20% down implies 5x leverage. Not saying that's what's causing the difference. But in the weird way leveraged finance works, a <100% income difference can absolutely fuel a 5x asset price gap.